We study the propagation and diffusion of electric charge fluctuations in the Bjorken hydrodynamic model with both white and Catteneo noise using purely numerical methods. We show that a lattice of noise fluctuations is required to fully calculate the two-point correlators of charge. We introduce a numerical procedure to solve the stochastic differential equations that arise from the charge conservation equation on the lattice event by event. We explicitly identify the self-correlation term in the case of Catteneo noise and provide a physical interpretation. We provide a numerical recipe to remove this contribution from the full two-point correlators. Finally, we calculate the balance functions for charged hadrons. By limiting the speed of signal propagation, we observe the expected narrowing of the balance functions after removing the self-correlations.
Bibliographical noteFunding Information:
A.D. thanks Gaurav Nirala for enlightening discussions. We thank Chun Shen for suggesting the jackknife method. This work was supported by the U.S. DOE Grant No. DE-FG02-87ER40328. C.P. acknowledges support from the CLASH project (KAW 2017-0036). The authors acknowledge the Minnesota Supercomputing Institute (MSI) at the University of Minnesota for providing resources that contributed to the research results reported within this paper.